In the S-category P (with compact-open strong shape mappings, cf. §1, instead of continuous mappings, and arbitrary finite-dimensional separable metrizable spaces instead of finite polyhedra) there exists according to [1], [2] an S-duality. The S-dual DX, X = (X,n) ∈ P, turns out to be of the same weak homotopy type as an appropriately defined functional dual (S0)X (Corollary 4.9). Sometimes th...

Arcfour is a stream cipher that produces a byte keystream B fbig i where a keyK is used to select the initial state S and the bi are produced by the state transition Si Si Let the byte length of K be jKj and let S K be the initial state produced by K Two keys K K are considered equivalent if S K S K and further K is weak if jK j jK j We show that there is a class of weak keys based on the notio...

Let T be a set of n triangles in three-dimensional space, let s be a line segment, and let t be a triangle, both disjoint from T . We consider the visibility map of s with respect to T , i.e., the portions of T that are visible from s. The visibility map of t is defined analogously. We look at two different notions of visibility: strong (complete) visibility, and weak (partial) visibility. The ...

Reliability and validity are crucial issues in research. Reliability is concerned with lowered quality of data due to random errors in measurement. Validity is concerned with whether variables measure what they purport to measure or are biased by other systemic factors, excluding random errors. Strength of correlation is limited by reliability. Given the problems in measuring reliability and va...

In the preceding chapters, the effects of lensing were so strong as to leave an unmistakable imprint on a specific source, allowing a detailed treatment. However, only the densest regions of the universe are able to provide such a spectacular lensing effect. To study more representative regions of the universe, we must examine large numbers of sources statistically. This is the domain of weak l...

This paper is devoted to clarify the algorithmic definition of the weak stability boundary in the framework of the planar Restricted Three Body Problem. The role of the invariant hyperbolic manifolds associated to the central manifolds of the libration points L1 and L2, as boundary of the weak stability region, is shown.

We explain how any cofibrantly generated weak factorisation system on a category may be equipped with a universally and canonically determined choice of cofibrant replacement. We then apply this to the theory of weak ω-categories, showing that the universal and canonical cofibrant replacement of the operad for strict ω-categories is precisely Leinster’s operad for weak ω-categories.

Double no-touch options, contracts which pay out a fixed amount provided an underlying asset remains within a given interval, are commonly traded, particularly in FX markets. In this work, we establish model-free bounds on the price of these options based on the prices of more liquidly traded options (call and digital call options). Key steps are the construction of superand sub-hedging strateg...

In this paper we give a proof of the strong Goldbach conjecture by studying limit status of original continuous Godbach natural number sequence {3, 4, ..., GNL} generated by original continuous odd prime number sequence {3, 5, ..., p} when p → ∞, that is, GNL = p when p → ∞. It implies the weak Goldbach conjecture. If a prime p is defined as Goldbach prime when GNL = p then Goldbach prime is th...